1. Field of the Invention
The present invention relates to a method and an apparatus for receiving a Minimum Mean-Squared-Error (MMSE). More particularly, the present invention relates to a frequency-domain MMSE reception apparatus and a method thereof in a Single-Carrier Frequency Division Multiple Access (SC-FDMA) system, to which channel-encoding is applied.
2. Description of the Related Art
A Long Term Evolution (LTE)-advanced standard of the 3rd Generation Partnership Project (3GPP) adopts a Single-Carrier Frequency Division Multiple Access (SC-FDMA) scheme and not an Orthogonal Frequency Division Multiple Access (OFDMA) scheme as a multiple access scheme of an uplink. Among the SC-FDMA schemes, LTE adopts a Discrete Fourier Transform-Spreading (DFT-S) OFDMA scheme.
FIG. 1 a block diagram illustrating configurations of a transmitter and a Time-Domain Equalization (TDE) Minimum Mean-Squared-Error (MMSE) receiver in an SC-FDMA system according to the related art.
Referring to FIG. 1, different from an OFDMA scheme where a channel-encoded digital modulation symbol is allocated and detected in a frequency domain, in the DFT-SOFDMA scheme, a modulation symbol, which has been received by a User Equipment (UE) #1 and a UE #2, and channel-encoded in a time domain by turbo encoders 111 and 141, is transformed into a frequency-domain modulation symbol by DFT-spreading blocks 112 and 142. Then, bands are respectively allocated to terminals and the allocated bands are multiplexed by Inverse Fast Fourier Transform (IFFT) blocks 113 and 143. Thereafter, the frequency-domain modulation symbol is transmitted through the multiplexed bands.
Therefore, the reception end of the DFT-SOFDMA system performs Fast Fourier Transform (FFT) on a time-domain signal, which is received through antennas Ant #1 and Ant #N, through FFT blocks 121 and 151. Then, Inverse Discrete Fourier Transform (IDFT) blocks 122 and 152 discriminate between bands which have been allocated to the UEs in a frequency domain. Afterwards, the reception end of the DFT-SOFDMA system needs to detect a modulation symbol in a time domain through noise estimators 131 and 132, a covariance estimator 133, a Channel Impulse Response (CIR) estimator 134, a weight value computation unit 135, and a time-domain MMSE receiver 136. Thereafter, it needs to perform channel-decoding on the time-domain modulation symbol through turbo decoders 123 and 153.
At this time, time-domain MMSE receiver 136 separates a spatially-multiplexed transmission signal from a time-domain signal, to which the IDFT block coinciding with a band of each UE transforms the received signal. Thereafter, time-domain MMSE receiver 136 performs MMSE detection of a space domain, which combines signals of reception antennas, and performs MMSE Time-Domain Equalization (TDE) on a time-domain Channel Impulse Response (CIR). The dimension of a time-domain channel matrix Ĥt output from CIR estimator 134 increases depending on channel selectivity. Therefore, it is complex to implement time-domain MMSE receiver 136.
FIG. 2 is a block diagram illustrating a configuration of a Frequency-Domain Equalization (FDE) MMSE receiver in an SC-FDMA system according to the related art.
Referring to FIG. 2, a soft output of frequency-domain MMSE receiver 236 is the same as the soft output of time-domain MMSE receiver 136 illustrated in the SC-FDMA system of FIG. 1. The soft output is obtained through performing transformation to a time-domain by IDFT blocks 222 and 252 just after MMSE equalization and detection are performed for each subcarrier of a relevant user band in a frequency domain by frequency-domain MMSE receiver 236. Accordingly, the receiver of the DFT-SOFDMA system uses the illustrated configuration where MMSE is performed in a frequency domain and the IDFT blocks generate a time-domain soft output. In this case, apart from the IDFT blocks 222 and 252 being positioned after the MMSE (FDE), the configuration of the MMSE receiver is similar to that in FIG. 1. Therefore, a detailed description of the same configuration as in FIG. 1 will be omitted.
A modulation symbol vector s(u), which is channel-encoded for a user or a transmission signal u in a time domain, is defined by equation (1) below.s(u)=[s0(u) . . . sM-1(u)]T, u=1, 2  (1)
In equation (1), M represents the length of a transmission signal, and is equal to the magnitude of DFT/IDFT. In a case where U=2, U representing the number of transmission signals, and where N=2, N representing the number of reception antennas, will be described for the sake of equation development. The modulation symbol vector is transformed into a frequency-domain transmission signal vector x(u) through DFT, as defined by equation (2) below.x(u)=Fs(u)  (2)
In equation (2), F represents a DFT matrix for DFT-spreading. [F]k,n corresponding to an element (k,n) of the DFT matrix and [F−1]n,k corresponding to an element (n,k) of an IDFT matrix, which is an inverse matrix of the DFT matrix, are defined by equation (3) below.
                                                        [              F              ]                                      k              ,              n                                =                                    1                              M                                      ⁢                          ⅇ                                                -                  j                                ⁢                                                      2                    ⁢                    π                    ⁢                                                                                  ⁢                    nk                                    M                                                                    ,                                  ⁢                                            [                              F                                  -                  1                                            ]                                      n              ,              k                                =                                    1                              M                                      ⁢                          ⅇ                              j                ⁢                                                      2                    ⁢                    π                    ⁢                                                                                  ⁢                    nk                                    M                                                                    ,                                  ⁢        n        ,                  k          =          0                ,        1        ,        …        ⁢                                  ,                  M          -          1                                    (        3        )            
The transmission end of the DFT-SOFDMA system allocates a signal, which has been transformed into a frequency domain as described above, to a subcarrier. Thereafter, it transforms the signal allocated to the subcarrier back into a time-domain signal through IFFT, and transmits the time-domain signal.
The reception end of the DFT-SOFDMA system performs FFT on a received signal, to which noises are added while being transmitted over a wireless channel, and transforms the received signal into a frequency-domain received signal. Then, the reception end detects and equalizes the frequency-domain received signal for a subcarrier of an allocated band.
In order to examine a reception process in an environment of Multi-Input Multi-Output (MIMO) as well as Single-Input Single-output (SISO), a received signal vector rk is expressed for a subcarrier k by equation (4) below.rk=Hk xk+nk  (4)
In equation (4), xk≡[xk(1) xk(2)]T represents a (U×1) transmission signal vector, which is obtained by reconstructing frequency-domain transmission signal vector x(u) for subcarrier k.
      H    k    =            [                                                  h                              11                ,                k                                                                        h                              12                ,                k                                                                                        h                              21                ,                k                                                                        h                              22                ,                k                                                        ]        =          [                                                  h              k                              (                1                )                                                                        h              k                              (                2                )                                                        ]      represents a (N×U) frequency-domain channel matrix.
      n    k    =      [                                        n                          1              ,              k                                                                        n                          2              ,              k                                            ]  represents a (N×1) frequency-domain Additive White Gaussian Noise (AWGN) vector.
When the MMSE receiver is applied, a weight value Wk of an MMSE detector, a weight value fk(u) and a frequency-domain soft output yk of the MMSE FDE are given by equations (5) to (7) below, respectively.
                                          W            k                    =                                                    (                                                                                                    (                                                  H                          k                                                )                                            H                                        ⁢                                          H                      k                                                        +                                                            σ                      n                      2                                        ⁢                                          I                      U                                                                      )                                            -                1                                      ⁢                                          (                                  H                  k                                )                            H                                      ,                                  ⁢                              W            k                    =                      [                                                                                w                    k                                          (                      1                      )                                                                                                                                        w                    k                                          (                      2                      )                                                                                            ]                                              (        5        )                                                      Q            k                    =                      [                                                                                q                    k                                          (                      1                      )                                                                                        0                                                                              0                                                                      q                    k                                          (                      2                      )                                                                                            ]                          ,                                  ⁢                              q            k                          (              u              )                                =                                                    (                                                      w                    k                                          (                      u                      )                                                        ⁢                                      h                    k                                          (                      u                      )                                                                      )                            *                                                                                                                                    w                      k                                              (                        u                        )                                                              ⁢                                          h                      k                                              (                        u                        )                                                                                                              2                            +                              var                ⁢                                  {                                                                                    w                        k                                                  (                          u                          )                                                                    ⁢                                              h                        k                                                  (                                                      u                            _                                                    )                                                                                      +                                                                  w                        k                                                  (                          u                          )                                                                    ⁢                      n                                                        }                                                                                        (        6        )                                                      y            _                    k                =                              Q            k                    ⁢                      W            k                    ⁢                      r            k                                              (        7        )            
When IDFT is performed on a frequency-domain soft output for each user or transmission signal, a time-domain soft output {tilde over (s)}(u) is given by equation (8) below.{tilde over (s)}(u)=F−1y(u)≡c(u)s(u)+e(u)  (8)
In equation (8), c(u) represents a value corresponding to the bias of the time-domain MMSE receiver. e(u)=[e0(u) . . . eM-1(u)] represents a time-domain error vector. A Log-Likelihood Ratio (LLR), which is necessary for channel-decoding, may be generated from a time-domain soft output in various ways. However, an LLR is typically generated by using a distance |{tilde over (s)}(u)−s(u)| between the soft output and a modulation symbol according to an Euclidean algorithm.
For example, when an approximated simple LLR is used, an LLR of 16 Quadrature Amplitude Modulation (16 QAM) is defined by equations (9) and (10) below.
                                          LLR                          n              ,              0                                      (              u              )                                =                                    SINR                              (                u                )                                      ⁢                          {                                                min                  ⁡                                      (                                                                  d                                                  I                          ,                                                      +                            1                                                                                              ,                                              d                                                  I                          ,                                                      +                            3                                                                                                                )                                                  -                                  min                  ⁡                                      (                                                                  d                                                  I                          ,                                                      -                            1                                                                                              ,                                              d                                                  I                          ,                                                      -                            3                                                                                                                )                                                              }                                      ⁢                                  ⁢                              LLR                          n              ,              1                                      (              u              )                                =                                    SINR                              (                u                )                                      ⁢                          {                                                min                  ⁡                                      (                                                                  d                                                  Q                          ,                                                      +                            1                                                                                              ,                                              d                                                  Q                          ,                                                      +                            3                                                                                                                )                                                  -                                  min                  ⁡                                      (                                                                  d                                                  Q                          ,                                                      -                            1                                                                                              ,                                              d                                                  Q                          ,                                                      -                            3                                                                                                                )                                                              }                                      ⁢                                  ⁢                              LLR                          n              ,              2                                      (              u              )                                =                                    SINR                              (                u                )                                      ⁢                          {                                                min                  ⁡                                      (                                                                  d                                                  I                          ,                                                      +                            3                                                                                              ,                                              d                                                  I                          ,                                                      -                            3                                                                                                                )                                                  -                                  min                  ⁡                                      (                                                                  d                                                  I                          ,                                                      +                            1                                                                                              ,                                              d                                                  I                          ,                                                      -                            1                                                                                                                )                                                              }                                      ⁢                                  ⁢                              LLR                          n              ,              3                                      (              u              )                                =                                    SINR                              (                u                )                                      ⁢                          {                                                min                  ⁡                                      (                                                                  d                                                  Q                          ,                                                      +                            3                                                                                              ,                                              d                                                  Q                          ,                                                      -                            3                                                                                                                )                                                  -                                  min                  ⁡                                      (                                                                  d                                                  Q                          ,                                                      +                            1                                                                                              ,                                              d                                                  Q                          ,                                                      -                            1                                                                                                                )                                                              }                                                          (        9        )                                                                    d                              I                ,                                  +                  1                                                      =                                          {                                                      Re                    ⁡                                          (                                                                        s                          ~                                                n                                                  (                          u                          )                                                                    )                                                        +                                      1                                          10                                                                      }                            2                                ,                                    d                              Q                ,                                  +                  1                                                      =                                          {                                                      Im                    ⁡                                          (                                                                        s                          ~                                                n                                                  (                          u                          )                                                                    )                                                        +                                      1                                          10                                                                      }                            2                                      ⁢                                  ⁢                                            d                              I                ,                                  +                  3                                                      =                                          {                                                      Re                    ⁡                                          (                                                                        s                          ~                                                n                                                  (                          u                          )                                                                    )                                                        +                                      3                                          10                                                                      }                            2                                ,                                    d                              Q                ,                                  +                  3                                                      =                                          {                                                      Im                    ⁡                                          (                                                                        s                          ~                                                n                                                  (                          u                          )                                                                    )                                                        +                                      3                                          10                                                                      }                            2                                      ⁢                                  ⁢                                            d                              I                ,                                  -                  1                                                      =                                          {                                                      Re                    ⁡                                          (                                                                        s                          ~                                                n                                                  (                          u                          )                                                                    )                                                        -                                      1                                          10                                                                      }                            2                                ,                                    d                              Q                ,                                  -                  1                                                      =                                          {                                                      Im                    ⁡                                          (                                                                        s                          ~                                                n                                                  (                          u                          )                                                                    )                                                        -                                      1                                          10                                                                      }                            2                                      ⁢                                  ⁢                                            d                              I                ,                                  -                  3                                                      =                                          {                                                      Re                    ⁡                                          (                                                                        s                          ~                                                n                                                  (                          u                          )                                                                    )                                                        -                                      3                                          10                                                                      }                            2                                ,                                    d                              Q                ,                                  -                  3                                                      =                                          {                                                      Im                    ⁡                                          (                                                                        s                          ~                                                n                                                  (                          u                          )                                                                    )                                                        -                                      3                                          10                                                                      }                            2                                                          (        10        )            
Accordingly, an optimal channel-decoding performance is achieved when error vector e(u) is equal to the AWGN vector and c(u)=1, so that a Minimum Error Probability (MEP) condition may be satisfied. AWGN modeling may typically be usually performed on error vector e(u) even when there is interference, assuming that a whitening filter is applied to error vector e(u). However, bias c(u) of an MMSE receiver is typically not equal to ‘1.’ Therefore, bias c(u) satisfies an MMSE condition, but does not satisfy the MEP condition. As a result, when channel-decoding is considered, the performance of the receiver is unavoidably degraded.
It is complex to implement a time-domain MMSE receiver depending on channel selectivity in a reception end of a channel-encoded SC-FDMA system. Therefore, an SC-FDMA signal is typically received by using a frequency-domain MMSE receiver and IDFT blocks, which output the same time-domain soft output as the time-domain MMSE receiver outputs. However, the time-domain soft output, which is provided by the frequency-domain MMSE receiver and IDFT blocks, includes the bias of the time-domain MMSE. Therefore, the time-domain soft output satisfies an MMSE condition, but does not satisfy the MEP condition. In this regard, a problem arises in that the bias of the time-domain MMSE receiver degrades the performance of an overall SC-FDMA receiver, which considers channel-decoding, when the configuration of the frequency-domain MMSE receiver is used.
Hence, a receiver of a channel-encoded system needs an unbiased soft output, which satisfies not only the MMSE condition but also the MEP condition, for optimal channel-decoding.
Therefore, a need exists for a frequency-domain unbiased MMSE reception apparatus and a method thereof, which can improve channel-decoding performance in an environment of MIMO as well as SISO.